Automatic Generation of Logical Models with AGES

We describe a new tool, AGES, which can be used to automatically generate models for order-sorted first-order theories. The tool uses linear algebra techniques to associate finite or infinite domains to the different sorts. Function and predicate symbols are then interpreted by means of piecewise interpretations with matrix-based expressions and inequalities. Relations interpreting binary predicates can be specified to be well-founded as an additional requirement for the generation of the model. The system is available as a web application.

[1]  José Meseguer,et al.  Operational termination of conditional term rewriting systems , 2005, Inf. Process. Lett..

[2]  Jian Zhang Constructing finite algebras with FALCON , 2004, Journal of Automated Reasoning.

[3]  Bruno Dutertre,et al.  Yices 2.2 , 2014, CAV.

[4]  Salvador Lucas,et al.  Proving Termination Properties with mu-term , 2010, AMAST.

[5]  Enno Ohlebusch,et al.  Advanced Topics in Term Rewriting , 2002, Springer New York.

[6]  Raúl Gutiérrez,et al.  Use of logical models for proving infeasibility in term rewriting , 2018, Inf. Process. Lett..

[7]  Hao Wang,et al.  Logic of many-sorted theories , 1952, Journal of Symbolic Logic.

[8]  Hans Zantema,et al.  Matrix Interpretations for Proving Termination of Term Rewriting , 2006, Journal of Automated Reasoning.

[9]  Raúl Gutiérrez,et al.  Automatic Synthesis of Logical Models for Order-Sorted First-Order Theories , 2018, Journal of Automated Reasoning.

[10]  Nikolaj Bjørner,et al.  Z3: An Efficient SMT Solver , 2008, TACAS.

[11]  José Meseguer,et al.  Dependency pairs for proving termination properties of conditional term rewriting systems , 2017, J. Log. Algebraic Methods Program..

[12]  Markus Lohrey,et al.  Compression of Rewriting Systems for Termination Analysis , 2013, RTA.

[13]  Salvador Lucas,et al.  Proving Program Properties as First-Order Satisfiability , 2018, LOPSTR.

[14]  Salvador Lucas,et al.  Using Well-Founded Relations for Proving Operational Termination , 2019, Journal of Automated Reasoning.

[15]  Albert Oliveras,et al.  The Barcelogic SMT Solver , 2008, CAV.

[16]  José Meseguer,et al.  Models and Equality for Logical Programming , 1987, TAPSOFT, Vol.1.

[17]  Jürgen Giesl,et al.  Mechanizing and Improving Dependency Pairs , 2006, Journal of Automated Reasoning.

[18]  Hantao Zhang,et al.  System Description: Generating Models by SEM , 1996, CADE.